Conventional digital correlation techniques are described in standard radar textbooks, such as Nathanson, Radar Design Principles, and Skolnick, Introduction to Radar Systems. Digital range correlation is described in commonly assigned U.S. Pat. No. 4,989,009.
A conventional range correlator 20 useful for target detection is shown in FIG. 1, and includes a transmitter 22 which produces a transmit signal modulated by modulator 24 with a reference word 32. The transmit signal is radiated toward the target and reflected to the receiver 26. The receiver output signal is provided to a correlator 30. The correlator includes a delay 34, a multiply 36 and a summer 38 for summing over a word length. The delayed reference word is multiplied with the receiver output signal. The output of the summer is provided to a processor for target detection.
For a received signal with zero Doppler shift, the receiver output signal has amplitude +A or -A, depending on the sample time and the value of the bit in the word sequence. The reference word 32 in the correlator 30 has amplitude +1 or -1, depending on the sequence of bits in the reference word. When the receiver output signal and the delayed reference word are aligned in time (i.e., when the target range delay is equal to the correlator delay provided by delay 34), the output of the multiplier is +A, (+A times +1=+A, or -A time -1=+A) over the entire word length. The output samples from the multiplier add together to maximize the sum over the word length. When the received signal and the delayed reference word 32 are not aligned in time, the output of the multiplier is +A or -A. Over the word length, the output samples from the multiplier add or subtract, so the summation over the word length by summer 38 is smaller than the maximum correlation peak.
When the received signal has a Doppler frequency shift Fd, the signal sample at time t, into the correlator is not simply .+-.A, but varies sinusoidally, .+-.A sin (2.pi.Fdt). The sinusoidal variation changes the amplitude and polarity of the signal samples, so the correlator output is degraded when the signal has non-zero Doppler frequency shift. The degradation for a correlated signal and an uncorrelated signal are illustrated in FIG. 2.
The output of the summer 38 for a correlated signal decreases as the Doppler frequency increases, while the output of the summer for an uncorrelated signal increases as the Doppler frequency increases. The ability to distinguish between correlated and uncorrelated signals is degraded as the signal Doppler frequency shift increases. In addition, the conventional correlator 30 with output at the word repetition rate has essentially white noise at the output, so the signal-to-noise ratio of the correlated signal decreases as the signal Doppler frequency increases.
The correlation degradation with Doppler shift can be further explained by examining the correlation operation in the frequency domain. For steady state periodic modulation, FIGS. 3A-3C respectively show the signal line spectra for a correlated signal and an uncorrelated signal at the input to the summer 38, and FIG. 3C shows the response of the summer in the frequency domain. The correlated signal into the summer 38 is a constant amplitude sinusoid so there is only one spectral line at the signal Doppler frequency Fd. The uncorrelated signal is wideband with many sidebands at .+-.Fd from the repetition rate and its harmonics. The summer response to a sinusoid decreases as the frequency increases, with nulls at the repetition rate and harmonics, and sidelobe peaks between the nulls. When the signal Doppler shift is zero, the sidebands of the uncorrelated signal fall at the repetition rate and harmonics at the nulls of the summer. For non-zero Doppler shift, the sidebands of the uncorrelated signal move out of the summer nulls and degrade the ability to reject uncorrelated signals.